tl;dr game preservation is struggling, and company-side game preservation often sucks.
Often you discover that a game you played long ago is no longer available in an official capacity, so you try to find it, and find that somewhat seedy sites are hosting them, and it gets worse the newer the game is. Why is this? Back then, game companies made their games on cartridges and disks, as well as arcade boards. These weren't easily reproducible by the average joe and pirates preferred bootleg cartridges and disks with modded consoles, nor were they publicly archived by said companies during the beginnings of the internet for fear of rampant piracy.
Because of how game history is being lost at such a rampant rate (due to unwitting disk gouges, corrosion on cartridges and arcade board failures), historians joined together to actually keep these games from being lost to time, becoming more virtuous versions of their pirate counterparts. But there's a new problem, one that needed more than just preserving the game files...
The problem initially showed up with MUDs, or Multi User Dungeoncrawlers and other online games back in the days of dialup supremacy. These games would let you fight alongside others in a bid for glory or the completion of mission objectives. These were hosted on centralized servers that relayed information from everyone to everyone else to make a cohesive world. The concept was expanded by MMOs, or Massive Multiplayer Online games, with a popular subgenre being MMORPGs (role playing games).
Then we see "live service" games, which are smaller than MMOs but still hold the world together through centralized servers. What do all these games have in common? Shutdowns. Ultimately, financial situations and/or lack of interest make these games close its doors, never to be played again because you can no longer reach the main or regional server, where your life's work was stored as a player. This is where private servers came in.
A private server is a server that either reverse-engineered how the game's online functions work and/or stole the server files, hosted for players to get back on a game they had lost access to, with two shut down examples being GunZ The Duel and Lego Universe. However, there's a catch. Like piracy, the law in most countries don't like private servers, but the existence of one is in a legal gray area. As long as you don't profit from the server, you're fine. The moment you make a cent more than necessary to keep the server running the law will hound you out of your gains.
Then there are specific demands made by companies that act as mafia-styled protection rackets. Lego (the publishers of Lego Universe, not the devs), demanded that a server have a very professional moderation team and strict server rules that befit their internal company requirements if you want more than 20 players on a server at once unless you want to get hounded. Some companies don't even care and will kill your not-for-profit server project without remorse (NAMELY ATLUS!).
Legally, not a lot. If you aren't cleanly reverse-engineering the server functions, or the software you acquired didn't do that, the game company will force you to stop everything you're doing regarding it, known in legalese as a Cease and Desist. If you are making excess money off of running a server for a game you love you'll likely get shut down that way too, and the company will probably go for the jugular anyways, again, notably Atlus.
If lawyers aren't your type or said lawyers are violent zealots, you'll need to set up defenses galore, or maybe hire the services of someone in a nation that doesn't really care about private servers. A more difficult alternative is to make a game that's inspired by your favorite game, with enough style differences (and some mechanical ones) to avoid incurring the wrath of said lawyers in the accusation of copying their company's game.
Honestly, thinking about this makes me realize that publishers are becoming more and more soulless by the day. It's all down to the brass tacks of their profit margin nowadays, and devs are being stripped of their will to make absolute bangers because they're forced ahead like slaves. Sad, really.
Game developers had more freedom because publishers let them cook back then. Nowadays? [(censored) RAW!!] as Gordon Ramsay would say, because the publishers basically made a more stressful version of Hell's Kitchen. Shame on the publishers rushing their dev teams, shame on Epic for killing indie companies financially, shame on us for allowing it.